Packages to enable Estonian ID-card support are available from the Arch User Repository. This article explains how to install the official software versions by AS Sertifitseerimiskeskus.
pcscd.socket using systemd.
Web authentication & digital signatures
Native Messaging host for Google Chrome/Chromium and Firefox and it is the modern way of doing authentication and digital signatures on the web.AUR package contains
For Google Chrome and Chromium you also will probably want to run esteid-update-nssdb script that enables TLS client authentication in the browser.
If you still can't login from Firefox with your ID-card you should installAUR.
ID-card and Digidoc utilities
The ID-card utility packages areAUR and AUR, with dependencies AUR and AUR.
These applications will automatically appear in your application menus. You can also start from command line with qdigidocclient and qesteidutil.